1996/12/08 by Robert C. Myers, Robert Myers, Robert P. Myers +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT
paper · pdf · doi:10.48550/arxiv.math/9612215
openalex publication_date 1996/12/08 · arxiv created 1996/12/09 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An irreducible open 3-manifold W is \bf R2-irreducible if every proper plane in W splits off a halfspace. In this paper it is shown that if such a W is the universal cover of a connected, \bf P2-irreducible open 3-manifold M with finitely generated fundamental group, then either W is homeomorphic to \bf R3 or the group is a free product of infinite cyclic groups and infinite closed surface groups. Given any such finitely generated group uncountably many M are constructed with that fundamental group such that their universal covers are \bf R2-irreducible, are not homeomorphic to \bf R3, and are pairwise non-homeomorphic. These results are related to the conjecture that closed, orientable, irreducible, aspherical 3-manifolds are covered by \bf R3.